Skew information-based coherence generating power of quantum channels

TL;DR

This paper introduces a measure for the ability of quantum channels to generate coherence, based on skew information, providing analytical formulas, bounds, and examples for various channels.

Contribution

It defines a new coherence generating power measure using skew information, with explicit formulas and bounds for arbitrary quantum channels, including unitary and qubit channels.

Findings

Derived analytical formulas for CGP of unitary channels.

Established bounds for convex combinations of channels.

Provided exact calculations for specific quantum gates and qubit channels.

Abstract

We study the ability of a quantum channel to generate quantum coherence when it applies to incoherent states. We define the measure of coherence generating power (CGP) for a generic quantum channel to be the average coherence generated by the quantum channel acting on a uniform ensemble of incoherent states based on the skew information-based coherence measure. We present explicitly the analytical formulae of the CGP for any arbitrary finite dimensional unitary channels. We derive the mean value of the CGP over the unitary groups and investigate the typicality of the normalized CGP. Furthermore, we give an upper bound of the CGP for the convex combinations of unitary channels. Detailed examples are provided to calculate exactly the values of the CGP for the unitary channels related to specific quantum gates and for some qubit channels.